Method and apparatus for optimizing fragmentation of boundaries for optical proximity correction (OPC) purposes

ABSTRACT

The present invention is directed to a method and apparatus for optimizing fragmentation of integrated circuit boundaries for optical proximity correction (OPC) purposes. The present invention may balance the number of vertices and the “flexibility” of the boundary and may recover fragmentation according to the process intensity profile along the ideal edge position to obtain the best decision for OPC.

CROSS-REFERENCE TO RELATED DOCUMENTS

The present application is a divisional of U.S. patent application Ser.No. 10/739,460, filed Dec. 18, 2003, which is herein incorporated byreference in its entirety. The present application herein incorporatesthe following by reference in their entirety: (1) U.S. patentapplication Ser. No. 09/879,664, entitled “Mask Correction forPhotolithographic Processes”, filed Jun. 12, 2001; and (2) N. Cobb,“Fast Optical and Process Proximity Correction Algorithms for IntegratedCircuit Manufacturing,” Ph.D. Thesis, Department of ElectricalEngineering and Computer Sciences, University of California at Berkeley,May 1998.

FIELD OF THE INVENTION

The present invention generally relates to the field of integratedcircuits, and particularly to a method and apparatus for optimizingfragmentation of boundaries for optical proximity correction (OPC)purposes.

BACKGROUND OF THE INVENTION

With the advance of technology in integrated circuits (ICs), the minimumfeature sizes of ICs have been shrinking for years. Commensurate withthis size reduction, various process limitations have made ICfabrication more difficult. One area of fabrication technology in whichsuch limitations have appeared is photolithography. Photolithographyinvolves selectively exposing regions of a resist coated silicon waferto a radiation pattern, and then developing the exposed resist in orderto selectively protect regions of wafer layers (e.g., regions ofsubstrate, polysilicon, or dielectric).

An integral component of a photolithographic apparatus is a “mask” or“reticle” which includes a pattern corresponding to features at onelayer in an IC design. Such reticle may typically include a transparentglass plate covered with a patterned light blocking material such aschromium. The reticle may be placed between a radiation source producingradiation of a pre-selected wavelength and a focusing lens which mayform part of a “stepper” apparatus. Placed beneath the stepper may be aresist covered silicon wafer. When the radiation from the radiationsource is directed onto the reticle, light may pass through the glass(regions not having chromium patterns) and project onto the resistcovered silicon wafer. In this manner, an image of the reticle may betransferred to the resist. The resist (sometimes referred to as a“photoresist”) is provided as a thin layer of radiation-sensitivematerial that is spin-coated over the entire silicon wafer surface.

As light passes through the reticle, the light may be refracted andscattered by the chromium edges. This may cause the projected image toexhibit some rounding and other optical distortion. While such effectspose relatively little difficulty in layouts with large feature sizes(e.g., layouts with critical dimensions above about 1 micron), theeffects may not be ignored in layouts having features smaller than about1 micron. The problems become especially pronounced in IC designs havingfeature sizes near the wavelength of light used in the photolithographicprocess. Optical distortions commonly encountered in photolithographymay include rounded corners, reduced feature widths, fusion of densefeatures, shifting of line segment positions, and the like.Unfortunately, any distorted illumination pattern may propagate to adeveloped resist pattern and ultimately to IC features such aspolysilicon gate regions, vias in dielectrics, and the like. As aresult, the IC performance may be degraded or the IC may becomeunusable.

To remedy this problem, a reticle correction technique known as opticalproximity correction (“OPC”) has been developed. Optical proximitycorrection may involve adding regions to and/or subtracting regions froma reticle design at locations chosen to overcome the distorting effectsof diffraction and scattering. Typically, OPC is performed on a digitalrepresentation of a desired IC pattern. First, the digital pattern maybe evaluated with software to identify regions where optical distortionwill result. Then the optical proximity correction may be applied tocompensate for the distortion. The resulting pattern may be ultimatelytransferred to the reticle glass. OPC may add various “corrections” tobase features. For example, some correction may take the form of“serifs,” which are small appendage-type addition or subtraction regionstypically made at corner regions on reticle designs. These “serifs” mayhave the intended effect of “sharpening” the corners of the illuminationpattern on the wafer surface.

With OPC, the boundary of an IC design often needs to be moved and/ordistorted. In order to get a better correction, it is often useful tointroduce more vertices on the boundary to give the IC designer morefreedom to design the IC. However, as the number of the vertices grows,the complexity of the masks (thus the cost) may grow. In addition,during the OPC process the fragment of the boundary edge often moves atan essential distance from its initial position, resulting in morecomplex structure with higher density than the initial design. This maycause different process intensity.

Therefore, it would be desirable to provide a method and apparatus foroptimizing fragmentation of boundaries for OPC purposes, which maybalance the number of vertices and the “flexibility” of the boundary andmay recover fragmentation according to the process intensity profilealong the ideal edge position to obtain the best decision for OPC.

SUMMARY OF THE INVENTION

Accordingly, the present invention is directed to a method and apparatusfor optimizing fragmentation of boundaries for optical proximitycorrection (OPC) purposes. The present invention may balance the numberof vertices and the “flexibility” of the boundary and may recoverfragmentation according to the process intensity profile along the idealedge position to obtain the best decision for OPC.

In an exemplary aspect of the present invention, a method for optimizingfragmentation of integrated circuit boundaries for optical proximitycorrection (OPC) purposes may include the following steps: (a) providinga segment S of an integrated circuit boundary and a neighborhood of theintegrated circuit boundary as input, the segment S having a first end Band a second end E; (b) placing elements (B,0) and (E,0) into a set Ms,an element in the set Ms having a first component representing a pointon the segment S and a second component representing a numeric value;(c) when a length of the segment S is not less than(D_(min)+2·D_(serif)), placing elements (B_(serif),0) and (E_(serif),0)into the set Ms, wherein B_(serif) is a beginning serif point on thesegment S with a distance between B and B_(serif) being equal toD_(serif), E_(serif) is an end serif point on the segment S with adistance between E and E_(serif) being equal to D_(serif), D_(serif) isa serif size for the segment S, and D_(min) is a minimal alloweddistance between any two fragmentation points on the segment S; (d)projecting at least one vertex, other than B and E, of the integratedcircuit boundary and the neighborhood to the segment S to form at leastone projection point P with a corresponding distance D between a vertexand the segment S; (e) when P lies on the segment S, adding an element(P,D) to the set Ms; (f) when an element (P′,D′) of the set Ms is suchthat a distance between the point P′ and the point B or between thepoint P′ and the point E is less than D_(min), and when the point P′ isneither the point B nor the point E, removing the element (P′,D′) fromthe set Ms; (g) when the element (B_(serif),0) is in the set Ms, when anelement (P_(i), D_(i)) of the set Ms is such that the point P_(i) liesbetween B and B_(serif), and when another element (P_(i)′, D_(i)′) ofthe set Ms is such that a distance between the point P_(i)′ and the endB_(serif) is less than D_(min), removing the element (B_(serif),0) fromthe set Ms; (h) when the element (E_(serif),0) is in the set Ms, when anelement (P_(i)″,D_(i)″) of the set Ms is such that the point P_(i)″ liesbetween E and E_(serif), and when another element (P_(i) ′″, D_(i)′″) ofthe set Ms is such that a distance between the point P_(i)′″ and the endE_(serif) is less than D_(min), removing the element (E_(serif),0) fromthe set Ms; (i) searching for a unworkable element for all elements ofthe set Ms; and (j) when no unworkable element is found for all elementsof the set Ms, defining first components of elements in the set Ms asfragmentation points for the segment S.

In an additional exemplary aspect of the present invention, a method forperforming mask edge fragmentation of an integrated circuit design edgemay include the following steps: (a) making initial edge fragmentationof an IC design edge; (b) performing an aerial image calculation of theIC design edge; (c) building process intensity profiles at ideal edgepositions along the IC design edge; (d) selecting new fragmentationpoints for the IC design edge; and (e) changing edge fragmentation ofthe IC design edge.

It is to be understood that both the foregoing general description andthe following detailed description are exemplary and explanatory onlyand are not restrictive of the invention as claimed. The accompanyingdrawings, which are incorporated in and constitute a part of thespecification, illustrate an embodiment of the invention and togetherwith the general description, serve to explain the principles of theinvention.

BRIEF DESCRIPTION OF THE DRAWINGS

The numerous advantages of the present invention may be betterunderstood by those skilled in the art by reference to the accompanyingfigures in which:

FIG. 1 illustrates a flowchart showing an exemplary method foroptimizing fragmentation of boundaries for optical proximity correction(OPC) purposes in accordance with the present invention;

FIG. 2 shows an exemplary segment of an IC boundary and itsneighborhood;

FIG. 3 shows exemplary segment ends and beginning and end serif pointson the segment shown in FIG. 2 in accordance with the present invention;

FIG. 4 shows exemplary projection points on the segment shown in FIG. 3in accordance with the present invention;

FIG. 5 shows the result after the projection points too close tosegments ends are removed from the segment shown in FIG. 4 in accordancewith the present invention;

FIG. 6 shows the result after the beginning serif point and the endserif point are removed from the segment shown in FIG. 5 in accordancewith the present invention;

FIG. 7 shows the result after an unworkable point is removed from thesegment shown in FIG. 6 in accordance with the present invention;

FIG. 8 shows fragmentation points after all unworkable points areremoved from the segment shown in FIG. 6 in accordance with the presentinvention;

FIG. 9 is a flowchart showing an exemplary method for performing maskedge fragmentation in accordance with the present invention; and

FIG. 10 is an illustration useful in explaining the steps illustrated inFIG. 9.

DETAILED DESCRIPTION OF THE INVENTION

Reference will now be made in detail to the presently preferredembodiments of the invention, examples of which are illustrated in theaccompanying drawings.

Referring first to FIG. 1, a flowchart showing an exemplary method orprocess 100 for optimizing fragmentation of boundaries for opticalproximity correction (OPC) purposes in accordance with the presentinvention is shown. The process 100 may start with step 102 in which asegment of an IC boundary and the IC boundary's neighborhood areprovided. For example, a segment S of an IC boundary may be provided.The segment S may have two ends: B and E. A serif size for the segment Smay be denoted as D_(serif), and a minimal allowed distance between anytwo fragmentation points on the segment S may be denoted as D_(min).

Then, in step 104, both ends of the segment may be placed into a set Msand, when the length of the segment is not less than(D_(min)+2·D_(serif)), both a beginning serif point and an end serifpoint may be set on the segment and may also be placed into the set Ms.The element of the set Ms may take the form of a pair (P_(i), D_(i)),where a first component P_(i) is a point on the segment, and a secondcomponent D_(i) is a numeric value.

In the case of the segment S, elements (B,0) and (E,0) may be added tothe set Ms. When the length of the segment S is not less than(D_(min)+2·D_(serif)), a beginning serif point B_(serif) may be denotedas a point which lies on the segment S with a distance between B andB_(serif) being equal to D_(serif), an end serif point E_(serif) may bedenoted as a point which lies on the segment S with a distance between Eand E_(serif) being equal to D_(serif), and elements (B_(serif),0) and(E_(serif),0) may be added to the set Ms.

In step 106, all vertices other than the segment ends may be projectedto the segment, and when a projection point lies on the segment, theprojection point may be added to the set Ms. In the case of the segmentS, the projection of each vertex of the IC boundary and its neighborhoodmay define a distance from the vertex to the segment S. The distancefrom a vertex A to the segment S may be denoted as D_(A) and thecorresponding projection point may be denoted as P_(A). When P_(A) lieson the segment S, the element (P_(A), D_(A)) may be added to the set Ms.Thus, in the case of the segment S, after the step 106, the set Ms mayinclude the elements (B,0) and (E,0), the elements (B_(serif),0) and(E_(serif),0) (if applicable), and one or more elements (P_(A), D_(A))(if applicable). In the following steps of the process 100,fragmentation points of the segment S may be selected from the set Ms.

In step 108, points too close to the segment ends may be removed fromthe set Ms. In the case of the segment S, if an element (P_(i), D_(i))(other than B and E) of the set Ms is such that a distance between P_(i)and B or between P_(i) and E is less than D_(min), the element (P_(i),D_(i)) may be deleted from the set Ms.

Next, in step 110, an inquiry of whether a beginning serif point and anend serif point have been set on the segment may be performed. If theanswer is no, the process 100 may proceed to step 114; if the answer isyes, the process 100 may proceed to step 112.

In the step 112, the beginning serif point and the end serif point maybe removed from the set Ms. In the case of the segment S, if an element(P_(i), D_(i)) of the set Ms is such that the point P_(i) lies between Band B_(serif), and if another element (P_(i)′, D_(i)′) of the set Ms issuch that a distance between P_(i)′ and B_(serif) is less than D_(min),the element (B_(serif),0) may be removed from the set Ms. Similarly, inthe case of the segment S, if an element (P_(i), D_(i)) of the set Ms issuch that the point P_(i) lies between E and E_(serif), and if anotherelement (P_(i)′, D_(i)′) of the set Ms is such that a distance betweenP_(i)′ and E_(serif) is less than D_(min), the element (E_(serif),0) maybe removed from the set Ms.

Next, in the step 114, a search for a “unworkable element” for allelements (except the segment ends) of the set Ms may be performed.

In the case of the segment S, in step 114-1, an element (P₁, D₁) of theset Ms may be selected, where the point P₁ is closest to the segment endB (but not B). If another element (P_(i), D_(i)) of the set Ms is suchthat a distance between P₁ and P_(i) is less than D_(min), then theelement (P₁, D₁) may be marked as a “unworkable element,” this distancemay be denoted as D_(unworkable), and the distance D₁ may be denoted asD_(unworkable) ^(priority). Then, in step 114-2, an element (P₂, D₂) ofthe set Ms may be selected, where the point P₂ is closest to the pointP₁ and the element (P₂, D₂) differs from the elements (B,0), (E,0) and(P₁, D₁). If another element (P_(i), D_(i)) of the set Ms is such that adistance between P₂ and P_(i) is less than D_(unworkable) or such that adistance between P₂ and P_(i) is equal to D_(unworkable), but D₂ isgreater than D_(unworkable) ^(priority), then the element (P₂, D₂) maybe marked as a “unworkable element,” this distance may be denoted asD_(unworkable), and the distance D₂ may be denoted as D_(unworkable)^(priority). Next, an element (P₃, D₃) of the set Ms may be selected,where the point P₃ is closest to the point P₂ and the element (P₃, D₃)differs from the elements (B,0), (E,0), (P₁, D₁), and (P₂, D₂). Then thestep 114-2 may be repeated. The step 114 may be performed for allelements of the set Ms except the elements (B,0) and (E,0).

Then in step 116, an inquiry of whether a unworkable element has beenfound may be performed. If the answer is yes, the last marked unworkableelement may be deleted from the set Ms in step 118, and the process 100returns to the step 114; if the answer is no (i.e., no element of theset Ms has been marked as “unworkable element”), then the firstcomponents of the elements of the set Ms may be defined as fragmentationpoints for the segment.

FIGS. 2 through 8 show the results after various steps of the presentmethod are performed on an exemplary segment S of an IC boundary inaccordance with an exemplary embodiment of the present invention. FIG. 2shows an exemplary segment S of an IC boundary and its neighborhood.FIG. 3 shows exemplary segment ends B and E and a beginning serif pointB_(serif) and an end serif point E_(serif) on the segment S shown inFIG. 2 in accordance with the present invention. FIG. 4 shows exemplaryprojection points on the segment S shown in FIG. 3 in accordance withthe present invention. FIG. 5 shows the result after the projectionpoints too close to the segment ends B and E are removed from thesegment S shown in FIG. 4 in accordance with the present invention. FIG.6 shows the result after the beginning serif point B_(serif) and the endserif point E_(serif) are removed from the segment S shown in FIG. 5 inaccordance with the present invention. FIG. 7 shows the result after anunworkable point is removed from the segment S shown in FIG. 6 inaccordance with the present invention. FIG. 8 shows fragmentation pointsafter all unworkable points are removed from the segment S shown in FIG.6 in accordance with the present invention.

It is understood that the segment S shown in FIGS. 2 through 8 isexemplary only and not intended as a structural limitation to thepresent invention. Those of ordinary skill in the art will understandthat the present invention may be applied to various segments of an ICboundary without departing from the scope and spirit of the presentinvention.

Referring now to FIG. 9, a flowchart showing an exemplary method orprocess 900 for performing mask edge fragmentation in accordance withthe present invention is shown. The process 900 may start with step 902in which initial edge fragmentation is performed and a number i_(number)is given a value “zero” (i_(number)=0), where i_(number) is the numberof iterations performed. In a preferred embodiment, initial edgefragmentation is performed based on the projection of vertices of thedesign's boundaries, as shown in FIG. 1. Aerial image calculation orprocess intensity calculation may be performed 904. For example, theprocess intensity calculation may be performed as:${I( {x,\quad y,\quad\overset{arrow}{a}} )}\quad = \quad{{\frac{1}{I_{0}}{\int{\int{J( {x_{u},\quad y_{u}} )}}}}❘{{E( {x,y,\quad x_{u},\quad y_{u},\quad\overset{arrow}{a}} )}❘^{2}{{\mathbb{d}x_{u}}{\mathbb{d}y_{u}}}}}$where I₀ is open frame intensity; andJ(x_(u),y_(u))is the intensity distribution at the source surface.

When i_(number) is less than a pre-set value I₀, in step 906 intensityiterations for OPC process may be performed, and i_(number) is increasedby 1. In a preferred embodiment, intensity iterations for OPC processmay be performed as shown in U.S. patent application Ser. No.09/879,664, entitled “Mask Correction for Photolithographic Processes”,filed Jun. 12, 2001. The result of the step 906 is an OPC decision closeto the optimal one. Then the process 900 returns to the step 904.

When i_(number) is greater than the pre-set value I₀, in step 914iterations for OPC process may be performed, and i_(number) is increasedby 1. The step 914 may be preferably the same as the step 906. Then theprocess 900 returns to the step 904.

When i_(number) is equal to the pre-set value I₀, process intensityprofiles at ideal edge positions may be built 908. The step 908 may berealized by calculation of process intensity values at the set of edgecontrol points, which are the control points for the cost function ofthe iteration process (see, e.g., FIG. 10). A region of intensity signchanging may be defined as follows:

-   -   a) if Δ_(i)=I(p_(i))−C⁰>0 and Δ_(i+1)=I(p_(i+1))−C⁰<0, i=1, . .        . , P_(edge)−1, then the (p_(i), p_(i+1)) is the sign changing        region of the edge;    -   b) if Δ_(i)=I(p_(i))−C⁰<0 and Δ_(i+1)=I(p_(i+1))−C⁰>0, i=1, . .        . , P_(edge)−1, then the (p_(i), p_(i+1)) is the sign changing        region of the edge; and    -   c) if I(p_(i−1))<0, I(p_(i))=0 and I(p_(i+1))>0, or if        I(p_(i−1))>0, I(p_(i))=0 and I(p_(i+1))<0, i=1, . . . ,        P_(edge)−1, then p_(i) is the sign changing point,        where I(p_(i)) is the process intensity value at the i-th point        on the edge; C⁰ is the desired intensity value (cutline of the        aerial image contour); and P_(edge) is the number of control        points on the edge.

When a distance between control points is small (e.g., 0.1-0.3 ofwavelength), the curve of the light intensity along the edge betweenpoints p_(i) and p_(i+1) may be presumed to change linearly. Thus, forthe foregoing cases a) and b), linear approximation may be used for adistance between a sign changing point and the point p_(i):$\bigtriangleup\quad = \quad\frac{| {{I( p_{i} )} - C^{0}} \middle| {\cdot {detlaP}} }{| {{I( p_{i} )} - C^{0}} \middle| {+ | {{I( p_{i + 1} )} - C^{0}} |} }$where deltaP is the distance between control points p_(i) and p_(i+1)along the segment. Thus, new fragmentation points corresponding to thenew design process intensity may be found. These new points may be addedto the list of fragmentation points for the segment.

New fragmentation points may be selected from the list of fragmentationpoints for the segment 910. Denote the minimal allowed distance betweenthe fragmentation points as D_(min). It is noted that this distanceD_(min) is chosen so that the distance between any pair of the pointsare greater than D_(min). For each new point added to the list in thestep 908, distances between this point and its neighbors may be checked.If a distance between this point and one neighbor point is less thanD_(min), the neighbor point need be deleted from the list. As a result,the list of fragmentation points for the segment may define thefragmentation points for the edge. Then, in step 912, edge fragmentationis changed and i_(number) is increased by 1. Next, the process 900returns to the step 904.

It is to be noted that the above described embodiments according to thepresent invention may be conveniently implemented using conventionalgeneral purpose digital computers programmed according to the teachingsof the present specification, as will be apparent to those skilled inthe computer art. Appropriate software coding may readily be prepared byskilled programmers based on the teachings of the present disclosure, aswill be apparent to those skilled in the software art.

It is to be understood that the present invention may be convenientlyimplemented in forms of software package. Such a software package may bea computer program product which employs a storage medium includingstored computer code which is used to program a computer to perform thedisclosed function and process of the present invention. The storagemedium may include, but is not limited to, any type of conventionalfloppy disks, optical disks, CD-ROMS, magneto-optical disks, ROMs, RAMs,EPROMs, EEPROMs, magnetic or optical cards, or any other suitable mediafor storing electronic instructions.

It is understood that the specific order or hierarchy of steps in theprocesses disclosed is an example of exemplary approaches. Based upondesign preferences, it is understood that the specific order orhierarchy of steps in the processes may be rearranged while remainingwithin the scope of the present invention. The accompanying methodclaims present elements of the various steps in a sample order, and arenot meant to be limited to the specific order or hierarchy presented.

It is believed that the present invention and many of its attendantadvantages will be understood by the foregoing description. It is alsobelieved that it will be apparent that various changes may be made inthe form, construction and arrangement of the components thereof withoutdeparting from the scope and spirit of the invention or withoutsacrificing all of its material advantages. The form herein beforedescribed being merely an explanatory embodiment thereof, it is theintention of the following claims to encompass and include such changes.

1. A method for performing mask edge fragmentation of an integratedcircuit design edge, comprising steps of: (a) making initial edgefragmentation of an IC design edge; (b) performing an aerial imagecalculation of said IC design edge; (c) building process intensityprofiles at ideal edge positions along said IC design edge; (d)selecting new fragmentation points for said IC design edge; and (e)changing edge fragmentation of said IC design edge.
 2. The method ofclaim 1, wherein said step (c) comprising: (c1) defining a sign changingregion of said IC design edge as follows: (c11) when Δ_(i)=I(p_(i))−C⁰>0and Δ_(i+1)=I(p_(i+1))−C⁰<0, i=1, . . . , P_(edge)−1, then (p_(i),p_(i+1)) is said sign changing region of said IC design edge; (c12) whenΔ_(i)=I(p_(i))−C⁰<0 and Δ_(i+1)=I(p_(i+1))−C⁰>0, i=1, . . . ,P_(edge)−1, then (p_(i), p_(i+1)) is said sign changing region of saidIC design edge; and (c13) when I(p_(i−1))<0, I(p_(i))=0 andI(p_(i+1))>0, or when I(p_(i−1))>0, I(p_(i))=0 and I(p_(i+1))<0, i=1, .. . , P_(edge)−1, then p_(i) is a sign changing point, wherein I(p_(i))is a process intensity value at an i-th point on said IC design edge; C⁰is a desired intensity value (cutline of an aerial image contour); andP_(edge) is a number of control points on said IC design edge; and (c2)adding new fragmentation points corresponding to a new design processintensity of said IC design edge to a list of fragmentation points ofsaid IC design edge.
 3. The method of claim 2, wherein said step (d)comprising: (d1) for one of said new fragmentation points, checking adistance between said one of said new fragmentation points and aneighbor point; and (d2) when said distance between said one of said newfragmentation points and said neighbor point is less than apredetermined value, deleting said neighbor point from said list.
 4. Themethod of claim 3, wherein said step (e) is performed based on saidlist.
 5. A computer-readable medium having computer-executableinstructions for performing a method for performing mask edgefragmentation of an integrated circuit design edge, said methodcomprising steps of: (a) making initial edge fragmentation of an ICdesign edge; (b) performing an aerial image calculation of said ICdesign edge; (c) building process intensity profiles at ideal edgepositions along said IC design edge; (d) selecting new fragmentationpoints for said IC design edge; and (e) changing edge fragmentation ofsaid IC design edge.
 6. The computer-readable medium of claim 5, whereinsaid step (c) comprising: (c1) defining a sign changing region of saidIC design edge as follows: (c11) when Δ_(i)=I(p_(i))−C⁰>0 andΔ_(i+1)=I(p_(i+1))−C⁰<0, i=1, . . . , P_(edge)−1, then (p_(i), p_(i+1))is said sign changing region of said IC design edge; (c12) whenΔ_(i)=I(p_(i))−C⁰<0 and Δ_(i+1)=I(p_(i+1))−C⁰>0, i=1, . . . ,P_(edge)−1, then (p_(i), p_(i+1)) is said sign changing region of saidIC design edge; and (c13) when I(p_(i−1))<0, I(p_(i))=0 andI(p_(i+1))>0, or when I(p_(i−1))>0, I(p_(i))=0 and I(p_(i+1))<0, i=1, .. . , P_(edge)−1, then p_(i) is a sign changing point, wherein I(p_(i))is a process intensity value at an i-th point on said IC design edge; C⁰is a desired intensity value (cutline of an aerial image contour); andP_(edge) is a number of control points on said IC design edge; and (c2)adding new fragmentation points corresponding to a new design processintensity of said IC design edge to a list of fragmentation points ofsaid IC design edge.
 7. The computer-readable medium of claim 6, whereinsaid step (d) comprising: (d1) for one of said new fragmentation points,checking a distance between said one of said new fragmentation pointsand a neighbor point; and (d2) when said distance between said one ofsaid new fragmentation points and said neighbor point is less than apredetermined value, deleting said neighbor point from said list.
 8. Thecomputer-readable medium of claim 7, wherein said step (e) is performedbased on said list.